The sum of the first n terms of an arithmetic progression is 252.
If the first term is -16 and the last is 72, the number of terms is the series is.
A. 6
B. 7
C. 8
D. 9
Correct Answer: D
Explanation
To solve for the number of terms (\(n\)) in the arithmetic progression, we can use the formula for the sum of the first \(n\) terms:
\[
S_n = \frac{n}{2} \times (a + l)
\]
Where:
- \(S_n\) is the sum of the first \(n\) terms
- \(a\) is the first term
- \(l\) is the last term
- \(n\) is the number of terms
Given:
- \(S_n = 252\)
- \(a = -16\)
- \(l = 72\)
Substituting the values into the formula:
\[
252 = \frac{n}{2} \times (-16 + 72)
\]
Simplifying:
\[
252 = \frac{n}{2} \times 56
\]
Multiply both sides by 2 to eliminate the fraction:
\[
504 = 56n
\]
Solve for \(n\):
\[
n = \frac{504}{56} = 9
\]
Thus, the number of terms in the series is D. 9.